A perturbation-incremental method for the calculation of semi-stable limit cycles of strongly non-linear oscillators

Research output: Journal Publications and ReviewsRGC 22 - Publication in policy or professional journal

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  • S. H. Chen
  • J. K H Chan
  • A. Y T Leung


Original languageEnglish
Pages (from-to)301-313
Journal / PublicationCommunications in Numerical Methods in Engineering
Issue number5
Publication statusPublished - 2000


The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form ẍ + g(x) = λf(x, ẋ, μ)ẋ is studied by the perturbation-incremental method. Firstly, the ordinary differential equation is transformed into an integral equation by a non-linear time transformation, then the initial solution for λ ≈ 0 is obtained by using the perturbation method. Secondly, the solution for an arbitrary value of λ can be determined by using the incremental approach. Two examples are given to show the efficiency and accuracy of the present method. Copyright © 2000 John Wiley & Sons, Ltd.

Research Area(s)

  • Perturbation-incremental method, Semi-stable limit cycles, Strongly non-linear oscillators